Yes, filing a separate state return will avoid double taxation.
If you file a joint Illinois return, you will have to include your total income on the joint return (including your wife's Canadian income).
Illinois does not allow a credit for Canadian taxes: "Taxes that qualify for the credit are income taxes you paid to another state of the United States, the District of Columbia, the Commonwealth of Puerto Rico, or any territory or possession of the United States, or to a political subdivision (e.g., county, city, local) of one of these jurisdictions. No credit is allowed for taxes paid to the federal government or to foreign countries or to their political subdivisions."
Schedule CR IL-1040 Instructions
Married filing separately
You can file a joint federal return (and claim a foreign tax credit or deduction) and file a separate Illinois return.
Follow this link: How do I prepare a joint federal return and separate state returns?
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